CAT 2026 Preparation: Day 9 – Profit and Loss, Miscellaneous DI Sets and Reading Skills

Part 1: Quantitative Aptitude - Profit and Loss

Profit and Loss is an extension of the concept of percentages, which forms the foundation of Arithmetic. Before solving CAT Profit and Loss questions, understand the basic terms and formulas. The following diagram illustrates the relationship between cost price, marked price, and selling price. The Percentage topic is a useful prerequisite.

• The price paid to purchase an article is its cost price (CP).
• The price that we mark or print on the article is the marked price (MP).
• The price at which an article is sold is its selling price (SP).
• Markup percentage = $\frac{MP-CP}{CP}\times100$
• Discount percentage = $\frac{MP-SP}{MP}\times100$
• Profit percentage = $\frac{SP-CP}{CP}\times100$
• If $SP>CP$, the seller makes a profit.
• If $SP<CP$, the seller incurs a loss.
• If $SP=CP$, there is neither a profit nor a loss.

Common Types of CAT Profit and Loss Questions

• Questions involve direct calculation to find profit%, Discount% or Markup%.
• Questions in which values are given in terms of profit%, Discount% or Markup%.

Typically, two of these values are given, and the third must be calculated.

• Questions on successive discounts.
• Questions on actual weight and faulty weights.
• Questions based on adulteration.
• Questions based on basic formulas only, and many more.

Practise each question type separately before moving on to mixed problems.

CAT Quant Questions With Solutions / Profit and Loss CAT previous year questions

The following previous-year CAT questions illustrate how Profit and Loss concepts are tested.

Q1. If a seller gives a discount of 15% on the retail price, she still makes a profit of 2%. Which of the following ensures that she makes a profit of 20%?[CAT Question Paper 2017 Slot 1]

1. Give a discount of 5% on the retail price
2. Give a discount of 2% on the retail price.
3. Increase the retail price by 2%.
4. Sell at retail price

Answer: Option 4

A 15% discount means that if $MP=100$, then $SP=85$.

A 2% profit means that if $CP=100$, then $SP=102$.

The selling price in both representations must be equal. Equating them gives:

$SP=510$, $CP=500$, and $MP=600$.

For a 20% profit, the selling price must be $600$, which equals the marked (retail) price. Therefore, Option 4 is correct.

Question 2

Q2. On selling a pen at 5% loss and a book at 15% gain, Karim gains Rs. 7. If he sells the pen at 5% gain and the book at 10% gain, he gains Rs. 13. What is the cost price of the book in Rupees? [CAT Question Paper 2019, Slot 1]

1. 85
2. 95
3. 80
4. 100

Answer: Option 3

Let the cost price of the pen be $100x$ and that of the book be $100y$.

Case 1:

$-5x+15y=7$

Case 2:

$5x+10y=13$

Solving the equations gives $y=\frac45$.

Therefore, the book's cost price is $100y=100\times\frac45=\text{₹}80$.

Prerequisite Before Practising CAT Profit and Loss Questions :

Before practising CAT Profit and Loss questions, students should be comfortable with:

• Fractions
• Application of Percentage
• Approximation

Tips to Prepare for CAT Profit and Loss

1. Learning conversions from Application of Percentage to fractions is important for this topic also.
2. Practice questions based on Application of Percentage well.
3. You can use the following tricks to solve the particular type of question:
   • If two articles are sold at the same selling price, with a profit of $a%$ on one and a loss of $a\%$ on the other, the overall result is always a loss of $\frac{a^2}{100}\%$.
   • If $n$ articles are purchased at equal cost prices and sold at different profit or loss percentages, the overall profit or loss percentage is the arithmetic mean of those percentages, treating each loss percentage as negative.
   • In the questions of true weight/ false weight, the Selling Price has always been calculated on the reading while the Cost price has always been calculated on actual weight. After that compare the final selling price and final cost price to find profit or loss percent.
   • In the questions of successive discounts, use the concept of the successive percentage change.

References to Practice CAT Arithmetic Questions:

• Quantitative Aptitude book by Abhijit Guha.
• CAT previous year papers

Part 2: Logical Reasoning and Data Interpretation - Miscellaneous DI

Miscellaneous CAT Data Interpretation (DI) sets may include the following formats:

• Multi-Layered Pie Chart
• Double Bar Graphs
• Logic Based DI (most common in recent years)
• Combination of two or more types of graphs in a single DI

Examples include a table combined with a pie chart or a line graph combined with a bar graph.

Such graphs are used to represent more data on a single graph.

Data Interpretation is an important component of CAT and other management entrance exams.

Three Essentials for DI Preparation

• Understanding Charts and Graphs
• Understanding the logic or concept (More required in multi-layered DI and Caselet DI)
• Be good at calculations.

CAT Previous-Year Data Interpretation Questions

The multi-layered pie-chart below shows the sales of LED television sets for a big retail electronics outlet during 2016 and 2017. The outer layer shows the monthly sales during this period, with each label showing the month followed by the sales figure of that month. For some months, the sales figures are not given in the chart. The middle-layer shows quarter-wise aggregate sales figures (in some cases, aggregate quarter-wise sales numbers are not given next to the quarter). The innermost layer shows annual sales. It is known that the sales figures during the three months of the second quarter (April, May, June) of 2016 form an arithmetic progression, as do the three monthly sales figures in the fourth quarter (October, November, December) of that year. [CAT Question Paper 2018]

Q1. What is the percentage increase in sales in December 2017 as compared to the sales in December 2016?

1. 22.22
2. 38.46
3. 50.00
4. 28.57

Solution: Option 4

Sales in December 2017 = $500-150-170=180$.

Sales in Q4 of 2016 are in AP:

Sales in October 2016 = $100$.

Sales in November 2016 = $100+x$.

Sales in December 2016 = $100+2x$.

So,

$100+(100+x)+(100+2x)=360$

$300+3x=360$

$3x=60$

$x=20$

Sales in December 2016 = $100+2(20)=140$.

Percentage increase = $\frac{180-140}{140}\times100=28.57%$.

Q2. In which quarter of 2017 was the percentage increase in sales from the same quarter of 2016 the highest?

1. Q1
2. Q3
3. Q2
4. Q4

Answer: Option 1 (Q1)

Prerequisite:

Before practising CAT DI sets, students should be comfortable with:

• Averages, ratios, and percentages
• Pie charts, tables, and other forms of data representation
• Venn diagrams

Tips to Solve Miscellaneous DI Sets

• Read the graphs carefully.
• Interpret the data from each kind of graph separately and then use them.
• Solve small calculations mentally.
• Examine each question separately and solve the easy one first.
• Practice questions that involve more than 2 graphs in a single DI.
• Shortcuts in calculations using Vedic math

CAT 2026 Data Interpretation: How to Reconcile Data Across Multiple Charts

Miscellaneous Data Interpretation sets can present the same information through multiple layers, tables, or graphical representations. A value obtained from one part of a set may be needed to calculate an unknown value elsewhere. Candidates must therefore understand how the different components relate to one another rather than treating every chart as an independent question.

How to Verify Totals Across Different Levels of a Chart

In a multi-layered pie chart, monthly figures may contribute to quarterly totals, while quarterly totals contribute to annual sales. These relationships create useful checks for verifying calculations.

For example, if monthly sales figures are provided for some months and the quarterly total is known, the missing monthly value can be calculated by subtracting the known figures from the quarterly total.

The calculated value should then be checked against the annual total or any other relevant information provided in the chart.

Candidates should verify that:

• The monthly figures add up to the corresponding quarterly total.
• The quarterly totals are consistent with the annual total.
• Any missing value calculated from one layer agrees with the information in another layer.
• The units and periods being compared are the same.

These checks can help identify arithmetic errors before they affect subsequent questions.

How to Use Mathematical Relationships to Find Missing Data

Some DI sets provide incomplete information but include additional relationships that allow the missing values to be determined. For example, a question may state that three monthly sales figures follow an arithmetic progression.

If the first value is $a$ and the common difference is $d$, the three terms of the arithmetic progression are:

$a,\quad a+d,\quad a+2d$

If their total is $S$, then:

$a+(a+d)+(a+2d)=S$

Therefore,

$3a+3d=S$

The equation can be combined with any other information given in the set to determine the unknown values.

The important point is to use the stated mathematical relationship together with the available totals. Candidates should not assume that missing values can be determined from the graph alone.

Part 3: VARC - Strategies to Improve Reading Skills

Reading is a skill used in many contexts, from understanding everyday information to engaging with complex arguments.

People read newspapers, technical books, novels, and other material for different purposes. Effective reading involves understanding, interpreting, and retaining the information.

Why Are Reading Skills Important?

• Reading is an essential and basic building block for learning.
• In daily life, the need to read things such as street signs or prescriptions proves reading is also an important life skill.
• To reduce stress.
• To read efficiently while identifying the main argument and relevant supporting information. Avoid treating an extremely fast reading speed as the goal if comprehension suffers.
• Reading skills help readers distinguish important information from less relevant details.
• To build confidence.

How Reading Habits Help

• In increasing your vocabulary
• In lowering stress
• It will enhance your imagination and help you to solve long passages and LRDI sections.

Suggestions to Improve Reading Skills

1. The first step to improving your reading skills. The reading ability questions for CAT exam are to develop reading habits by reading any of the following:

2. Newspapers

   1. Magazines
   2. Novels from good writers
   3. Fiction and Non-Fiction books

3. Read the book of your interest.

4. Read the articles of interest.

5. Once the reading habit is developed, half of the work is done. Now start to analyse the information.

6. Always get an idea of every passage. Try to find out the keywords.

7. Always underline the important words or the words that are new to you.

8. Learn the underlined words and try to find an alternate for these words.

9. Try to find the uses of idioms and phrases while reading a novel or a book.

10. Try to avoid non-useful information while reading.

11. Such practices will lead to improved reading skills.

Suggested Reading

• The Secret by Rhonda Byrne
• Everything Happens for a Reason: And Other Lies I've Loved by Kate Bowler

CAT 2026 VARC Preparation: How to Measure Reading Comprehension Improvement

Developing a regular reading habit is an important part of CAT VARC preparation, but reading more material does not automatically translate into better comprehension. Candidates must also evaluate how well they understand an author's argument, identify relevant information, and interpret the passage accurately.

A structured review of reading practice can help aspirants recognise whether their comprehension is improving and identify the areas that still need attention.

How to Maintain a Reading Practice Record

After completing a reading passage or editorial, record a few details about the reading session. This provides a consistent basis for evaluating progress over time.

The objective is not to make every reading session a timed test. Instead, use the record to identify patterns and determine which aspects of reading require more focused practice.

How to Balance Reading Speed and Understanding

Reading quickly is useful only when the reader can retain and interpret the relevant information. If faster reading consistently leads to incorrect answers or an inability to explain the central argument, comprehension should take priority.

Candidates can begin by reading a passage at a comfortable pace and summarising its main argument in their own words. They can then gradually introduce time limits while checking whether the quality of their understanding remains consistent.

A useful practice routine is to:

1. Read a passage without repeatedly returning to earlier sentences.
2. Summarise the main argument in two or three sentences.
3. Identify the role of the major supporting points.
4. Answer a few questions based on the passage.
5. Review errors and determine whether they resulted from misreading, incomplete understanding, or unsupported interpretation.

This process makes it easier to distinguish a genuine comprehension problem from a simple lack of reading speed.

Shortcuts for CAT Profit and Loss Questions

Profit and Loss questions often test whether candidates can select the right formula and apply it efficiently. The following seven methods can help improve speed and accuracy.

1. Use the Basic Formulas

Profit or loss is the difference between the selling price (SP) and cost price (CP).

Profit or loss percentage is calculated by dividing the profit or loss amount by CP and multiplying by $100$.

Example: An item bought for ₹500 and sold for ₹600 earns a profit of ₹100. Therefore, profit percentage is $\frac{100}{500}\times100=20\%$.

2. Relate SP, CP, Profit Percentage, and Loss Percentage

Selling Price can be found by adjusting the Cost Price based on profit or loss percentage.

$SP=CP\left(1+\frac{\text{Profit}\%}{100}\right)$

$SP=CP\left(1-\frac{\text{Loss}\%}{100}\right)$

Example: If $CP=₹400$ and the profit is $25\%$, then $SP=400\left(1+\frac{25}{100}\right)=\text{₹}500$.

3. Calculate the Effective Discount for Successive Discounts

When multiple discounts are given one after the other, calculate the combined discount using the formula:

$\text{Effective discount}=1-(1-d_1)(1-d_2)$

Here, $d_1$ and $d_2$ are the discounts expressed as decimals.

Example: Successive discounts of $20%$ and $10%$ give an effective discount of $1-(1-0.20)(1-0.10)=0.28=28%$.

4. Assume the Cost Price Is 100

Taking CP as 100 simplifies calculations of profit or loss percentages.

Example: If $CP=100$ and the profit is $15\%$, then $SP=115$.

5. Find the Marked Price Using Profit and Discount

The marked price can be calculated by adjusting the cost price for profit and discount percentages.

$MP=\frac{CP\left(1+\frac{\text{Profit}\%}{100}\right)}{1-\frac{\text{Discount}\%}{100}}$

Example: If $CP=\text{₹}400$, profit is $20\%$, and discount is $10\%$, then $MP=\frac{400(1.20)}{0.90}=\text{₹}533.33$ (approximately).

6. Calculate Profit or Loss Percentage from the Difference

When profit or loss amount is known, divide it by the cost price and multiply by 100 to get the percentage.

Example: If $CP=\text{₹}250$ and $SP=\text{₹}225$, the loss is ₹25. The loss percentage is $\frac{25}{250}\times100=10\%$.

7. Handle Multiple Items Separately Before Combining

Calculate profit or loss on each item individually, then add or subtract to find overall profit or loss.

Example: A gain of ₹30 on one item and a loss of ₹20 on another result in a net gain of $30-20=₹10$.

CAT 2026 Profit and Loss: How to Solve Multi-Condition Questions Accurately

Profit and Loss questions in CAT can combine several conditions in a single problem. A question may involve a change in the selling price, a discount on the marked price, or different transactions involving multiple products. In these situations, the main challenge is to identify which values remain unchanged and which conditions apply to each transaction.

How to Identify the Relationship Between Different Transactions

Before calculating the answer, separate the information given in the question into individual conditions. This is particularly useful when two selling scenarios are compared or when the profit earned on one product is combined with the loss incurred on another.

For example, consider a question in which a seller earns a profit under one selling condition and a different profit after changing the selling price. The cost price may remain constant, even though the selling price changes. Identifying this distinction helps candidates establish the correct relationship between the two situations.

Use the following approach:

1. Identify the original transaction and record the relevant values.
2. Identify the condition that changes in the second transaction.
3. Determine which quantities remain constant across both situations.
4. Translate each condition into a separate mathematical relationship.
5. Solve the relationships together and check whether the result satisfies both conditions.

How to Detect Inconsistent or Incorrect Answers

A calculated answer should satisfy every condition stated in the question. Obtaining a numerical value is not sufficient if that value contradicts another part of the problem.

Candidates should check whether the calculated selling price corresponds to the stated profit or loss, whether a discount is applied to the correct marked price, and whether the final result is consistent with all the given transactions.

For multiple-product questions, verify the combined result instead of checking only one product in isolation. A correct individual calculation may still lead to an incorrect overall answer if the gains and losses are combined improperly.

CAT 2026 Preparation Resources

Access section-wise resources for VARC, DILR, and Quantitative Aptitude to strengthen your preparation and improve exam performance.